# Elongated triangular gyrobicupola

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Elongated triangular gyrobicupola
Rank3
TypeCRF
Notation
Bowers style acronymEtigybcu
Coxeter diagramoxxx3xxxo&#xt
Elements
Faces
Edges6+6+6+6+12
Vertices6+12
Vertex figures6 rectangles, edge lengths 1 and 2
12 isosceles trapezoids, edge lengths 1, 2, 2, 2
Measures (edge length 1)
Volume${\displaystyle {\frac {10{\sqrt {2}}+9{\sqrt {3}}}{6}}\approx 4.95510}$
Dihedral angles3–4 join: ${\displaystyle \arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }}$
4–4 join: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
3–4 cupolaic: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
4–4 prismatic: 120°
Central density1
Number of external pieces20
Level of complexity12
Related polytopes
ArmyEtigybcu
RegimentEtigybcu
ConjugateNone
Abstract & topological properties
Flag count144
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(G2×A1)/2, order 12
Flag orbits12
ConvexYes
NatureTame

The elongated triangular gyrobicupola (OBSA: etigybcu) is one of the 92 Johnson solids (J36). It consists of 2+6 triangles and 6+6 squares. It can be constructed by inserting a hexagonal prism between the two halves of the cuboctahedron, seen as a triangular gyrobicupola.

## Vertex coordinates

An elongated triangular gyrobicupola of edge length 1 has the following vertices:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \pm \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,{\frac {3+2{\sqrt {6}}}{6}}\right)}$,
• ${\displaystyle \pm \left(0,\,{\frac {\sqrt {3}}{3}},\,{\frac {3+2{\sqrt {6}}}{6}}\right)}$.